Trigonometric Ratios Table: Definition, Table Creation, Value Table and Functions Table with Steps

Trigonometric Ratios Table Overview

Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles. It is an essential tool for many disciplines such as physics, engineering, and astronomy. As such, it is important to have a good understanding of the different trigonometric ratios and the tables that are used to represent them. 

Trigonometric ratios tables are an essential tool for anyone studying trigonometry. These tables provide a quick and easy reference to the various trigonometric ratios, such as sine, cosine, and tangent, along with their corresponding angle measurements. The tables also include reciprocal ratios, such as cosecant, secant, and cotangent. By having a comprehensive trigonometric ratios table, you will be able to quickly and accurately solve any trigonometry problems you may encounter.

What is a Trigonometric Ratios Table?

A trigonometric ratios table is a mathematical tool that provides a quick and easy reference to trigonometric ratios, such as sine, cosine, and tangent, and their corresponding angle measurements. These tables are typically organized in a grid format, with the angles listed along the top row and the ratios listed down the side. The values in the table are ratios between 0 and 1, and can be used to calculate the size of an angle, the length of a side, or the area of a triangle.

How to Use a Trigonometric Ratios Table

Trigonometric ratios tables can be used to quickly and accurately solve any trigonometry problems. To use a trigonometric ratios table, first identify the type of ratio you are looking for (sine, cosine, tangent, etc.). Then look up the angle you are working within the top row of the table. Finally, match the angle to the appropriate ratio to find the value you need.

For example, if you are looking for the sine of an angle of 30 degrees, you would look in the top row of the table and find the angle of 30 degrees. Then, you would match it to the sine ratio and find the value of 0.5.

Difference between a Trigonometric Ratios Table and a Standard Trigonometry Table

The difference between a trigonometric ratios table and a standard trigonometry table is that the former includes the reciprocal ratios, such as cosecant, secant, and cotangent. These ratios are not commonly used in everyday calculations but are still useful for certain problems. For example, if you need to find the length of a side of a triangle, you will need to use the cotangent ratio.

Common Uses of a Trigonometric Ratios Table

Trigonometric ratios tables are used for a variety of applications. They are commonly used for solving problems in geometry, such as finding the area of a triangle or the length of a side. They can also be used to calculate the angle of a triangle given its sides or to find the angle of a right triangle given its two sides. Additionally, they can be used to calculate the height of a building given its angle and the length of the hypotenuse.

How to Create a Trigonometric Ratios Table

Creating a trigonometric ratios table is relatively simple. All you need is a calculator and a piece of paper. First, draw a grid on the paper with the angles listed along the top row and the ratios listed down the side. Then, use the calculator to find the values for each ratio for each angle. Finally, fill in the table with the corresponding values.

Below are the few steps to create the trigonometric ratios table

Step 1: Create a table

Create a table with the top row listing the angles such as 0°, 30°, 45°, 60°, 90°, and write all trigonometric functions in the first column such as sin, cos, tan, cosec, sec, cot.

Step 2: Determine the value of sin

To determine the values of sin, divide 0, 1, 2, 3, 4 by 4 under the root, respectively. See the example below.

To determine the value of sin 0°

04=0

Step 3:Determine the value of cos

The cos-value is the opposite angle of the sin angle. To determine the value of cos divide by 4 in the opposite sequence of sin. For example, divide 4 by 4 under the root to get the value of cos 0°. See the example below.

To determine the value of cos 0°

44=1

Step 4:Determine the value of tan

The tan is equal to sin divided by cos. tan = sin/cos. To determine the value of tan at 0° divide the value of sin at 0° by the value of cos at 0°. See the example below.

Tan 0°= 0/1 = 0

Similarly, the table would be.

Step 5:Determine the value of the cot

The value of the cot is equal to the reciprocal of tan. The value of cot at 0° will be obtained by dividing 1 by the value of tan at 0°. So the value will be:

Cot 0° = 1/0 = Infinite or Not Defined

The table for a cot is given below.

Step 6: Determine the value of cosec

The value of cosec at 0° is the reciprocal of sin at 0°.

cosec 0°= 1/0 = Infinite or Not Defined

The table for cosec is given below.

Step 7: Determine the value of sec

The value of sec can be determined by all reciprocal values of cos. The value of sec on 0° is the opposite of cos on 0°. So the value will be:

sec⁡0∘=11=1

In the same way, the table for sec is given below.

Trigonometric Ratios Table Value Examples

To illustrate how to use a trigonometric ratios table, let's look at some examples. For an angle of 45 degrees, the sine ratio is 0.707, the cosine ratio is 0.866, and the tangent ratio is 1.000. The cosecant ratio is 1.414, the secant ratio is 1.155, and the cotangent ratio is 0.866.

For an angle of 60 degrees, the sine ratio is 0.866, the cosine ratio is 0.500, and the tangent ratio is 1.732. The cosecant ratio is 0.707, the secant ratio is 2.000, and the cotangent ratio is 0.500.

Tips for Memorizing Trigonometric Ratios Table Values

Memorizing trigonometric ratios table values can be difficult, but there are some tricks that can help. First, focus on memorizing the angles that are multiples of 30 degrees, such as 0, 30, 60, 90, 120, etc. These angles are the most commonly used in trigonometry, so it is important to have a good understanding of them. The Trigonometry ratios table is dependent upon the trigonometry formulas.

Below is the table to memorize the trigonometry table. Before beginning, try to remember below trigonometry formulas.

Advanced Applications of a Trigonometric Ratios Table

Trigonometric ratios tables can be used for more than just solving problems in trigonometry. They can also be used to calculate the angles of a polygon, calculate the area of a circle, and solve problems involving vectors. Additionally, they can be used to solve problems involving the law of sines and the law of cosines.

Things to Remember

1. Trigonometric values are based on the three major trigonometric ratios: Sine, Cosine, and Tangent.
   Sine or sin θ = Side opposite to θ / Hypotenuse
   Cosines or cos θ = Adjacent side to θ / Hypotenuse
   Tangent or tan θ = Side opposite to θ / Adjacent side to θ
2. 0°, 30°, 45°, 60°, and 90° in a trigonometric table are called the standard angles in trigonometry.
3. The angle values of trigonometric functions cotangent, secant, cosecant in a trigonometric table, can also be calculated using these standard angles values of sine, cosecant, and tangent.
4. All the higher angle values of trigonometric functions such as 120°, 390°, can be easily calculated from the standard angle values in a trigonometry table.

Conclusion

Trigonometric ratios tables are an essential tool for anyone studying trigonometry. They can be used to quickly and accurately solve any trigonometry problem, and can also be used for advanced applications. We hope this blog article has helped you understand the power of the trigonometric ratios table and how it can be used to solve problems in trigonometry.

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